Though information theory and mathematical physics shared the same interest in entropy after the work of Boltzmann and Shannon, respectively. The taste is quite divergent.
In mathematical physics, heat equation is regarded to be quite well-studied and well-understood for hundred years and the attention has shifted to more complicated equations like Boltzmann equation and Landau damping [1]}. In information theory, to study a new channel or source model [2]}, the special case where the noise is Gaussian is usually discussed first. The main reason is that, Gaussian distribution matches entropy quite well (e.g., maximum entropy principle) and researchers can obtain some initial results in closed-form which will shed light on the cases with arbitrary noises. However, for some complicated communication scenarios in multi-user information theory, even Gaussian cases are hard to deal with; e.g., Gaussian interference channel [3]}, [4]}, has been notoriously open for over 40 years. Those long-standing open problems indicates that a cornerstone of information theory on the Gaussian distribution is missing.
